Linear dependent types in a call-by-value scenario
Linear dependent types were introduced recently (Dal Lago and Gaboardi, 2012) [26] as a formal system that allows to precisely capture both the extensional behavior and the time complexity of λ-terms, when the latter are evaluated by Krivine’s abstract machine. In this work, we show that the same pa...
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| Veröffentlicht in: | Science of computer programming Jg. 84; S. 77 - 100 |
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| Abstract | Linear dependent types were introduced recently (Dal Lago and Gaboardi, 2012) [26] as a formal system that allows to precisely capture both the extensional behavior and the time complexity of λ-terms, when the latter are evaluated by Krivine’s abstract machine. In this work, we show that the same paradigm can be applied to call-by-value computation. A system of linear dependent types for Plotkin’s PCF is introduced, called dℓPCFV, whose types reflect the complexity of evaluating terms in the CEK machine. dℓPCFV is proved to be sound, but also relatively complete: every true statement about the extensional and intentional behavior of terms can be derived, provided all true index term inequalities can be used as assumptions.
•A type system for complexity analysis of higher-order functional programs.•Extend previous, related, work to an applied, call-by-value, lambda-calculus.•The type system is not only sound, but relatively complete.•We provide fully-developed nontrivial examples of complexity analyses. |
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| AbstractList | Linear dependent types allow to precisely capture both the extensional behavior and the time complexity of λ-terms, when the latter are evaluated by Krivine's abstract machine. In this work, we show that the same paradigm can be applied to call-by-value computation. A system of linear dependent types for Plotkin's PCF is introduced, called dlPCFv whose types reflect the complexity of evaluating terms in the so-called CEK machine. dlPCFv is proved to be sound, but also relatively complete: every true statement about the extensional and intentional behavior of terms can be derived, provided all true index term inequalities can be used as assumptions. Linear dependent types were introduced recently (Dal Lago and Gaboardi, 2012) [26] as a formal system that allows to precisely capture both the extensional behavior and the time complexity of λ-terms, when the latter are evaluated by Krivine’s abstract machine. In this work, we show that the same paradigm can be applied to call-by-value computation. A system of linear dependent types for Plotkin’s PCF is introduced, called dℓPCFV, whose types reflect the complexity of evaluating terms in the CEK machine. dℓPCFV is proved to be sound, but also relatively complete: every true statement about the extensional and intentional behavior of terms can be derived, provided all true index term inequalities can be used as assumptions. •A type system for complexity analysis of higher-order functional programs.•Extend previous, related, work to an applied, call-by-value, lambda-calculus.•The type system is not only sound, but relatively complete.•We provide fully-developed nontrivial examples of complexity analyses. |
| Author | Petit, Barbara Dal Lago, Ugo |
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| Keywords | Linear logic Complexity analysis Type systems Implicit computational complexity |
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| Title | Linear dependent types in a call-by-value scenario |
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